Spherical Shock Waves: The Self-Similar Solution

Abstract

This particular chapter has an independent character and deals almost exclusively with Taylor’s analysis of very strong spherical shocks. The presentation follows Taylor’s analysis and notation in relation to the similarity solution for the point source explosion in air. Following his analysis, the partial differential equations in Eulerian form are reduced to a set of coupled ordinary differential equations which are numerically integrated. Taylor’s analytical approximations for the pressure, density and velocity are presented and these turn out to be remarkably accurate when compared to the numerical solutions. His analysis of the energy left in the atmosphere after the blast wave has propagated away has also been presented and discussed. The chapter concludes with an approximate treatment of very strong shock, which is based on the particular nature of the point source solution where most of the material is piled up at the shock front. An analytical solution of the coupled differential equations for the point source explosion in air concludes the chapter.